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In order to explore the magnetostrophic regime expected for planetary cores,experiments have been conducted in a rotating sphere filled with liquid sodium,with an imposed dipolar magnetic field (the DTS setup). The field is producedby a permanent magnet enclosed in an inner sphere, which can rotate at aseparate rate, producing a spherical Couette flow. The flow properties areinvestigated by measuring electric potentials on the outer sphere, the inducedmagnetic field in the laboratory frame, and velocity profiles inside the liquidsodium using ultrasonic Doppler velocimetry. The present article focuses on thetime-averaged axisymmetric part of the flow. The Doppler profiles show that theangular velocity of the fluid is relatively uniform in most of the fluid shell,but rises near the inner sphere, revealing the presence of a magnetic wind, andgently drops towards the outer sphere. The transition from a magnetostrophicflow near the inner sphere to a geostrophic flow near the outer sphere iscontrolled by the local Elsasser number. For Rossby numbers up to order 1, theobserved velocity profiles all show a similar shape. Numerical simulations inthe linear regime are computed, and synthetic velocity profiles are comparedwith the measured ones. In the geostrophic region, a torque-balance modelprovides very good predictions. We find that the induced magnetic field variesin a consistent fashion, and displays a peculiar peak in the counter-rotatingregime. This happens when the fluid rotation rate is almost equal and oppositeto the outer sphere rotation rate. The fluid is then almost at rest in thelaboratory frame, and the Proudman-Taylor constraint vanishes, enabling astrong meridional flow. We suggest that dynamo action might be favored in sucha situation.

Rapidly rotating spherical Couette flow in a dipolar magnetic field: an experimental study of the mean axisymmetric flow